LHS — Definition, Formula & Examples
LHS is short for Left-Hand Side, meaning everything to the left of the equals sign in an equation. For example, in , the LHS is .
In an equation of the form , the LHS refers to the expression — the entire expression that appears on the left side of the equality symbol.
How It Works
When you see "LHS" in a textbook or solution, it simply means "the left side of the equation." Teachers and textbooks use it as shorthand to refer to one side without rewriting the whole expression. For instance, saying "substitute into the LHS" tells you to plug the value into the left-side expression only. You then compare the result with the RHS (Right-Hand Side) to check whether the equation holds true.
Worked Example
Problem: Verify that is a solution of by evaluating the LHS.
Identify the LHS: The LHS is the expression to the left of the equals sign.
Substitute: Replace with in the LHS.
Compare with RHS: The RHS is . Since LHS RHS, the equation is satisfied.
Answer: The LHS equals 10, which matches the RHS, confirming is a solution.
Why It Matters
LHS and RHS appear constantly in algebra textbooks and standardized tests when describing equation-solving steps. Recognizing the abbreviation saves you from confusion when reading proofs, worked solutions, or instructions like "simplify the LHS."
Common Mistakes
Mistake: Confusing LHS with the answer or solution of an equation.
Correction: LHS is just the expression on the left side of the equals sign — it is not the solution. The solution is the value of the variable that makes LHS equal to RHS.